Duplicating and its Applications in Batch Scheduling

In this paper, we firstly describe a technique named Duplicating, which duplicates machines in batch scheduling environment. Then we discuss several applications of Duplicating in solving batch scheduling problems, for the batch scheduling problem on unrelated parallel machines to minimize makespan, we give an (4− 2 B )-approximation algorithm and an (2− 1 B + ǫ) algorithm when m is fixed. We also present an 4(2 − 1 B + ǫ)-competitive algorithm for the on-line scheduling problem on identical machines to minimize total weighted completion time.